A new approach for the anti-sway control of container cranes using coupled partial and ordinary differential equations is investigated. The dynamics of the hoisting rope is derived in the form of an axially moving cable equation, while the dynamics of the actuator is given in the form of an ODE. The control objective is to suppress the transverse vibrations of the load via a domain control. A control law based upon the Lyapunov's second method is derived. It is revealed that a time-varying control force and a suitable passive damping can successfully suppress the transverse vibrations. The exponential stability of the closed loop system is proved.